Question

determine whether the correlation coefficients show strong, moderate, or weak correlation.
$r = - 0.91$
$r = 0.82$
$r = - 0.49$
$r = 0.26$
$r = 0.54$
$r = - 0.18$
strong correlation
moderate correlation
weak correlation

Explanation:

Step1: Recall the criteria for correlation strength

The closer the absolute value of the correlation coefficient \(r\) is to \(1\), the stronger the correlation. If \(|r|\geq0.7\), it is a strong correlation. If \(0.4\leq|r|\lt0.7\), it is a moderate correlation. If \(|r|\lt0.4\), it is a weak correlation.

Step2: Analyze \(r = - 0.91\)

Calculate \(|r|=|-0.91| = 0.91\). Since \(0.91\geq0.7\), it is a strong correlation.

Step3: Analyze \(r = 0.82\)

Calculate \(|r|=|0.82|=0.82\). Since \(0.82\geq0.7\), it is a strong correlation.

Step4: Analyze \(r=-0.49\)

Calculate \(|r| = |-0.49|=0.49\). Since \(0.4\leq0.49\lt0.7\), it is a moderate correlation.

Step5: Analyze \(r = 0.26\)

Calculate \(|r|=|0.26|=0.26\). Since \(0.26\lt0.4\), it is a weak correlation.

Step6: Analyze \(r = 0.54\)

Calculate \(|r|=|0.54|=0.54\). Since \(0.4\leq0.54\lt0.7\), it is a moderate correlation.

Step7: Analyze \(r=-0.18\)

Calculate \(|r|=|-0.18|=0.18\). Since \(0.18\lt0.4\), it is a weak correlation.

Answer:

• Strong Correlation: \(r=-0.91\), \(r = 0.82\)
• Moderate Correlation: \(r=-0.49\), \(r = 0.54\)
• Weak Correlation: \(r = 0.26\), \(r=-0.18\)